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§1.4: equations & applications

Precalculus. §1.4: equations & applications. Finance, Interest Yield. Gold. g. 0.1. 0.1g. 0.04. Stocks. 150000 - g. 0.04(150000 – g). Total. 150000. 12000. Bennie has $150,000 to invest. Bennie has $150,000 to invest.

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§1.4: equations & applications

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  1. Precalculus §1.4: equations & applications

  2. Finance, Interest Yield Gold g 0.1 0.1g 0.04 Stocks 150000 - g 0.04(150000 – g) Total 150000 12000 Bennie has $150,000 to invest. Bennie has $150,000 to invest. Part of it will be invested in gold coins with which he expects to earn 10% interest. Part of it will be invested in gold coins with which he expects to earn 10% interest. He will invest the rest in stocks earning 4% interest. He will invest the rest in stocks earning 4% interest. If Bennie wants to earn $12,000, how much should he invest in each? If Bennie wants to earn $12,000, how much should he invest in each? 0.1g + 0.04(150000 – g) = 12000

  3. Answer • g = 100,000 • Benny should invest $100,000 in gold and $50,000 in stocks.

  4. Mixture pure syrup 1.0 s s 0.04 4% sol. 240 0.04(240) 12% sol. s + 240 0.12(s + 240) 0.12 Coca-colabottling machines are calibrated to mix syrup and soda water into an ideal 12% solution. Coca-colabottling machines are calibrated to mix syrup and soda water into an ideal 12% solution. A machine malfunctioned and mixed 240 gallons of a 4% solution. A machine malfunctioned and mixed 240 gallons of a 4% solution. How much pure syrup must be added to produce an acceptable beverage? How much pure syrup must be added to produce an acceptable beverage? s + 0.04(240) = 0.12(s + 240)

  5. Answer • s ≈ 21.82 gallons of syrup

  6. Uniform Motion against current 3.5 r - 40 3.5(r - 40) 2.25 with current r + 40 2.25(r + 40) A jet flies 3.5 hours against an air current of 40 mph. A jet flies 3.5 hours against an air current of 40 mph. It takes 2.25 hours to fly back with the same current. It takes 2.25 hours to fly back with the same current. How fast is the jet in still air? How fast is the jet in still air? 3.5(r - 40) = 2.25(r + 40)

  7. Answer • r ≈ 184 mph

  8. Extra Practice : Uniform Motion A boat heads downstream on a river having a current of 8 mph. The trip down takes 2 hrs, the trip back takes 3.5 hrs. How fast is the boat in still water? A bus leaves town going 55 mph. A taxi leaves ½ hr later to catch it going 70 mph. How long will it take the taxi to catch the bus? How far will it need to drive to do so? • Answers: • r = 29.3 mph • t = 1.83 h, d = 128 mi

  9. Extra Practice : Finance Mrs. Puff would like to invest $68,000 and earn 6% interest for her retirement from boating school. Krusty Krab bonds earn only 1.5% interest, but Chum Bucket bonds pay 9%. How much should she invest in each? The Bank of Bucks pays 2% interest on savings. The Bank of Dinero pays 3% on savings. Max has $9500 to put into savings. How much should Max save in each bank to earn $200 in interest? • Answers: • 9%: $40800, 1.5%: $27200 • BoB: $8500, BoD: $1000

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